Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator–prey model View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2012-11-09

AUTHORS

Rachel A. Taylor, Jonathan A. Sherratt, Andrew White

ABSTRACT

Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters—such as a peak in the birth rate in spring. It is important to understand how this seasonal forcing affects the population dynamics. The main way in which seasonal models have been studied is through a two dimensional bifurcation approach. We augment this bifurcation approach with extensive simulation in order to understand the potential solution behaviours for a predator–prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have either monotonic decay to the coexistence steady state, or oscillatory decay, or stable limit cycles. The range of behaviour the system can exhibit includes multi-year cycles of different periodicities, parameter ranges with coexisting multi-year cycles of the same or different period as well as quasi-periodicity and chaos. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced. We discuss how the methods could be extended to understand the dynamics of a wide range of ecological and epidemiological systems that are subject to seasonal changes. More... »

PAGES

1741-1764

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00285-012-0612-z

DOI

http://dx.doi.org/10.1007/s00285-012-0612-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019198304

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/23138231


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/06", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Biological Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0602", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Ecology", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Animals", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Biological Clocks", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Computer Simulation", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Ecosystem", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Models, Biological", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Population Dynamics", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Predatory Behavior", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Seasons", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK", 
          "id": "http://www.grid.ac/institutes/grid.9531.e", 
          "name": [
            "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Taylor", 
        "givenName": "Rachel A.", 
        "id": "sg:person.01123623344.09", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01123623344.09"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK", 
          "id": "http://www.grid.ac/institutes/grid.9531.e", 
          "name": [
            "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sherratt", 
        "givenName": "Jonathan A.", 
        "id": "sg:person.01010517364.85", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01010517364.85"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK", 
          "id": "http://www.grid.ac/institutes/grid.9531.e", 
          "name": [
            "Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "White", 
        "givenName": "Andrew", 
        "id": "sg:person.0640757150.29", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0640757150.29"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1038/364232a0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052255271", 
          "https://doi.org/10.1038/364232a0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/45223", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016279987", 
          "https://doi.org/10.1038/45223"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00285-004-0264-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053718643", 
          "https://doi.org/10.1007/s00285-004-0264-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00163027", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049290609", 
          "https://doi.org/10.1007/bf00163027"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-69909-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041529197", 
          "https://doi.org/10.1007/978-3-540-69909-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-2421-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010746307", 
          "https://doi.org/10.1007/978-1-4757-2421-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002850050174", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039821362", 
          "https://doi.org/10.1007/s002850050174"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02461847", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030190328", 
          "https://doi.org/10.1007/bf02461847"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02460293", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023317062", 
          "https://doi.org/10.1007/bf02460293"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-1140-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044255212", 
          "https://doi.org/10.1007/978-1-4612-1140-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-93048-5_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006519426", 
          "https://doi.org/10.1007/978-3-642-93048-5_1"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2012-11-09", 
    "datePublishedReg": "2012-11-09", 
    "description": "Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters\u2014such as a peak in the birth rate in spring. It is important to understand how this seasonal forcing affects the population dynamics. The main way in which seasonal models have been studied is through a two dimensional bifurcation approach. We augment this bifurcation approach with extensive simulation in order to understand the potential solution behaviours for a predator\u2013prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have either monotonic decay to the coexistence steady state, or oscillatory decay, or stable limit cycles. The range of behaviour the system can exhibit includes multi-year cycles of different periodicities, parameter ranges with coexisting multi-year cycles of the same or different period as well as quasi-periodicity and chaos. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced. We discuss how the methods could be extended to understand the dynamics of a wide range of ecological and epidemiological systems that are subject to seasonal changes.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00285-012-0612-z", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1081642", 
        "issn": [
          "0303-6812", 
          "1432-1416"
        ], 
        "name": "Journal of Mathematical Biology", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "6-7", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "67"
      }
    ], 
    "keywords": [
      "seasonal environmental changes", 
      "seasonal changes", 
      "prey growth rate", 
      "life history", 
      "population dynamics", 
      "environmental changes", 
      "predator\u2013prey system", 
      "multi-year cycles", 
      "coexistence steady state", 
      "natural systems", 
      "growth rate", 
      "predator\u2013prey model", 
      "species", 
      "seasonal forcing", 
      "large effect", 
      "cycle", 
      "range of behaviors", 
      "dynamics", 
      "wide range", 
      "spring", 
      "changes", 
      "population", 
      "epidemiological systems", 
      "level of oscillation", 
      "consequences", 
      "levels", 
      "range", 
      "different periods", 
      "bifurcation approach", 
      "system", 
      "rate", 
      "stable limit cycle", 
      "unforced dynamics", 
      "seasonal model", 
      "main ways", 
      "decay", 
      "effect", 
      "unforced system", 
      "approach", 
      "limit cycles", 
      "periodicity", 
      "steady state", 
      "oscillatory decay", 
      "behavior", 
      "model", 
      "monotonic decay", 
      "birth rate", 
      "solution behavior", 
      "history", 
      "different periodicities", 
      "extensive simulations", 
      "influence", 
      "state", 
      "period", 
      "order", 
      "peak", 
      "chaos", 
      "way", 
      "oscillations", 
      "method", 
      "affect", 
      "simulations", 
      "parameters", 
      "forcing", 
      "lessons"
    ], 
    "name": "Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator\u2013prey model", 
    "pagination": "1741-1764", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1019198304"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00285-012-0612-z"
        ]
      }, 
      {
        "name": "pubmed_id", 
        "type": "PropertyValue", 
        "value": [
          "23138231"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00285-012-0612-z", 
      "https://app.dimensions.ai/details/publication/pub.1019198304"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-12-01T06:29", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221201/entities/gbq_results/article/article_562.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00285-012-0612-z"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00285-012-0612-z'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00285-012-0612-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00285-012-0612-z'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00285-012-0612-z'


 

This table displays all metadata directly associated to this object as RDF triples.

216 TRIPLES      21 PREDICATES      109 URIs      90 LITERALS      15 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00285-012-0612-z schema:about N43da7a99bd944461b09c611b1ac023e5
2 N632496b62100461fa72b263a3b6f2f92
3 N71a83d054d5f4f5282979b1f7cb922e7
4 N7a41fcffe1514691ae21d09d99a0b34d
5 N8943df260fc04bb69a8bae546d008fd7
6 Nb8133b970edf4cf3b26402468b3bfcc1
7 Nd07b01d4219b4812934281eab6686ece
8 Nda0e8ff1dd114705b3f3ecdf2d8314de
9 anzsrc-for:06
10 anzsrc-for:0602
11 schema:author Ne581d61bdd9d4b8d9330393e93f47ba4
12 schema:citation sg:pub.10.1007/978-1-4612-1140-2
13 sg:pub.10.1007/978-1-4757-2421-9
14 sg:pub.10.1007/978-3-540-69909-5
15 sg:pub.10.1007/978-3-642-93048-5_1
16 sg:pub.10.1007/bf00163027
17 sg:pub.10.1007/bf02460293
18 sg:pub.10.1007/bf02461847
19 sg:pub.10.1007/s00285-004-0264-8
20 sg:pub.10.1007/s002850050174
21 sg:pub.10.1038/364232a0
22 sg:pub.10.1038/45223
23 schema:datePublished 2012-11-09
24 schema:datePublishedReg 2012-11-09
25 schema:description Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters—such as a peak in the birth rate in spring. It is important to understand how this seasonal forcing affects the population dynamics. The main way in which seasonal models have been studied is through a two dimensional bifurcation approach. We augment this bifurcation approach with extensive simulation in order to understand the potential solution behaviours for a predator–prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have either monotonic decay to the coexistence steady state, or oscillatory decay, or stable limit cycles. The range of behaviour the system can exhibit includes multi-year cycles of different periodicities, parameter ranges with coexisting multi-year cycles of the same or different period as well as quasi-periodicity and chaos. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced. We discuss how the methods could be extended to understand the dynamics of a wide range of ecological and epidemiological systems that are subject to seasonal changes.
26 schema:genre article
27 schema:isAccessibleForFree false
28 schema:isPartOf Nbffc403daf924d318a0110152e8cd05f
29 Nc17ef2ddd3f44c509bb668f06d478e49
30 sg:journal.1081642
31 schema:keywords affect
32 approach
33 behavior
34 bifurcation approach
35 birth rate
36 changes
37 chaos
38 coexistence steady state
39 consequences
40 cycle
41 decay
42 different periodicities
43 different periods
44 dynamics
45 effect
46 environmental changes
47 epidemiological systems
48 extensive simulations
49 forcing
50 growth rate
51 history
52 influence
53 large effect
54 lessons
55 level of oscillation
56 levels
57 life history
58 limit cycles
59 main ways
60 method
61 model
62 monotonic decay
63 multi-year cycles
64 natural systems
65 order
66 oscillations
67 oscillatory decay
68 parameters
69 peak
70 period
71 periodicity
72 population
73 population dynamics
74 predator–prey model
75 predator–prey system
76 prey growth rate
77 range
78 range of behaviors
79 rate
80 seasonal changes
81 seasonal environmental changes
82 seasonal forcing
83 seasonal model
84 simulations
85 solution behavior
86 species
87 spring
88 stable limit cycle
89 state
90 steady state
91 system
92 unforced dynamics
93 unforced system
94 way
95 wide range
96 schema:name Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator–prey model
97 schema:pagination 1741-1764
98 schema:productId N50861faabee24ddda479a16ec9024da4
99 N698fdc65000a4c498f143118114eb586
100 N69e9e35d411e4857a4acb7f15a40cb52
101 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019198304
102 https://doi.org/10.1007/s00285-012-0612-z
103 schema:sdDatePublished 2022-12-01T06:29
104 schema:sdLicense https://scigraph.springernature.com/explorer/license/
105 schema:sdPublisher Nd68a06998d9b4bfbb9e30980dff43a00
106 schema:url https://doi.org/10.1007/s00285-012-0612-z
107 sgo:license sg:explorer/license/
108 sgo:sdDataset articles
109 rdf:type schema:ScholarlyArticle
110 N43da7a99bd944461b09c611b1ac023e5 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
111 schema:name Biological Clocks
112 rdf:type schema:DefinedTerm
113 N50861faabee24ddda479a16ec9024da4 schema:name dimensions_id
114 schema:value pub.1019198304
115 rdf:type schema:PropertyValue
116 N632496b62100461fa72b263a3b6f2f92 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
117 schema:name Predatory Behavior
118 rdf:type schema:DefinedTerm
119 N695475c4738a4790b17baaa338738d79 rdf:first sg:person.0640757150.29
120 rdf:rest rdf:nil
121 N698fdc65000a4c498f143118114eb586 schema:name doi
122 schema:value 10.1007/s00285-012-0612-z
123 rdf:type schema:PropertyValue
124 N69e9e35d411e4857a4acb7f15a40cb52 schema:name pubmed_id
125 schema:value 23138231
126 rdf:type schema:PropertyValue
127 N71a83d054d5f4f5282979b1f7cb922e7 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
128 schema:name Seasons
129 rdf:type schema:DefinedTerm
130 N7a41fcffe1514691ae21d09d99a0b34d schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
131 schema:name Population Dynamics
132 rdf:type schema:DefinedTerm
133 N8943df260fc04bb69a8bae546d008fd7 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
134 schema:name Computer Simulation
135 rdf:type schema:DefinedTerm
136 Na7b2687399294f9a9e565a73b244fce9 rdf:first sg:person.01010517364.85
137 rdf:rest N695475c4738a4790b17baaa338738d79
138 Nb8133b970edf4cf3b26402468b3bfcc1 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
139 schema:name Models, Biological
140 rdf:type schema:DefinedTerm
141 Nbffc403daf924d318a0110152e8cd05f schema:volumeNumber 67
142 rdf:type schema:PublicationVolume
143 Nc17ef2ddd3f44c509bb668f06d478e49 schema:issueNumber 6-7
144 rdf:type schema:PublicationIssue
145 Nd07b01d4219b4812934281eab6686ece schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
146 schema:name Animals
147 rdf:type schema:DefinedTerm
148 Nd68a06998d9b4bfbb9e30980dff43a00 schema:name Springer Nature - SN SciGraph project
149 rdf:type schema:Organization
150 Nda0e8ff1dd114705b3f3ecdf2d8314de schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
151 schema:name Ecosystem
152 rdf:type schema:DefinedTerm
153 Ne581d61bdd9d4b8d9330393e93f47ba4 rdf:first sg:person.01123623344.09
154 rdf:rest Na7b2687399294f9a9e565a73b244fce9
155 anzsrc-for:06 schema:inDefinedTermSet anzsrc-for:
156 schema:name Biological Sciences
157 rdf:type schema:DefinedTerm
158 anzsrc-for:0602 schema:inDefinedTermSet anzsrc-for:
159 schema:name Ecology
160 rdf:type schema:DefinedTerm
161 sg:journal.1081642 schema:issn 0303-6812
162 1432-1416
163 schema:name Journal of Mathematical Biology
164 schema:publisher Springer Nature
165 rdf:type schema:Periodical
166 sg:person.01010517364.85 schema:affiliation grid-institutes:grid.9531.e
167 schema:familyName Sherratt
168 schema:givenName Jonathan A.
169 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01010517364.85
170 rdf:type schema:Person
171 sg:person.01123623344.09 schema:affiliation grid-institutes:grid.9531.e
172 schema:familyName Taylor
173 schema:givenName Rachel A.
174 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01123623344.09
175 rdf:type schema:Person
176 sg:person.0640757150.29 schema:affiliation grid-institutes:grid.9531.e
177 schema:familyName White
178 schema:givenName Andrew
179 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0640757150.29
180 rdf:type schema:Person
181 sg:pub.10.1007/978-1-4612-1140-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044255212
182 https://doi.org/10.1007/978-1-4612-1140-2
183 rdf:type schema:CreativeWork
184 sg:pub.10.1007/978-1-4757-2421-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010746307
185 https://doi.org/10.1007/978-1-4757-2421-9
186 rdf:type schema:CreativeWork
187 sg:pub.10.1007/978-3-540-69909-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041529197
188 https://doi.org/10.1007/978-3-540-69909-5
189 rdf:type schema:CreativeWork
190 sg:pub.10.1007/978-3-642-93048-5_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006519426
191 https://doi.org/10.1007/978-3-642-93048-5_1
192 rdf:type schema:CreativeWork
193 sg:pub.10.1007/bf00163027 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049290609
194 https://doi.org/10.1007/bf00163027
195 rdf:type schema:CreativeWork
196 sg:pub.10.1007/bf02460293 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023317062
197 https://doi.org/10.1007/bf02460293
198 rdf:type schema:CreativeWork
199 sg:pub.10.1007/bf02461847 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030190328
200 https://doi.org/10.1007/bf02461847
201 rdf:type schema:CreativeWork
202 sg:pub.10.1007/s00285-004-0264-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053718643
203 https://doi.org/10.1007/s00285-004-0264-8
204 rdf:type schema:CreativeWork
205 sg:pub.10.1007/s002850050174 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039821362
206 https://doi.org/10.1007/s002850050174
207 rdf:type schema:CreativeWork
208 sg:pub.10.1038/364232a0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052255271
209 https://doi.org/10.1038/364232a0
210 rdf:type schema:CreativeWork
211 sg:pub.10.1038/45223 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016279987
212 https://doi.org/10.1038/45223
213 rdf:type schema:CreativeWork
214 grid-institutes:grid.9531.e schema:alternateName Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK
215 schema:name Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, EH14 4AS, Edinburgh, UK
216 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...